Four spheres of radius 6 cm just fit inside a cylinder.

Calculate the volume inside the cylinder that is empty.

Leave your answer in terms of pi.

Answer:

El número obtenido es:

Step-by-step explanation:

Vamos a escoger tres números sencillos para cada variable como:

Por lo tanto, nuestro número de tres cifras es:

Ahora, nos dice que invirtamos los números a1 y c1, por lo tanto, nuestro nuevo número de tres cifras sería:

A continuación, nos menciona que restemos el menor del mayor, en este caso, nuestro número menor es 123 y el mayor es 321, por lo tanto:

Como obtuvimos el número 198, se podría decir que:

Ahora nos piden que invirtamos a2 y c2, por lo tanto nuestro nuevo número sería:

Y por último, nos solicita que sumemos los dos últimos números obtenidos, entonces tenemos:

Por lo tanto, el número obtenido al final es 1089, el cual obtendrás sin importar qué número de tres cifras elijas al inicio, siempre y cuando no se repitan el primero y el tercer dígito.

Answer:

Both a = −4 and a = −1 are true solutions

Step-by-step explanation:

Given

[tex]\sqrt{a + 5} = a + 3[/tex]

[tex]a = -4; a = -1[/tex]

Required

The true statement about the solutions

We have:

[tex]\sqrt{a + 5} = a + 3[/tex]

Square both sides

[tex]a + 5 = (a + 3)^2[/tex]

[tex]a + 5 =a^2 + 6a + 9[/tex]

Collect like terms

[tex]a^2 + 6a - a + 9 - 5 = 0[/tex]

[tex]a^2 + 5a + 4 = 0[/tex]

Expand

[tex]a^2 + 4a + a + 4 = 0[/tex]

Factorize

[tex]a(a + 4) + 1(a + 4) = 0[/tex]

Factor out a + 4

[tex](a + 1)(a + 4) = 0[/tex]

Split:

[tex]a + 1 = 0; a + 4 = 0[/tex]

Solve:

[tex]a =-1; a = -4[/tex]

Answer:

C on 3dge

Step-by-step explanation:

Both a = −4 and a = −1 are true solutions

Answer:

12/20, or 3/5

Step-by-step explanation:

To find the probability of Raymond not picking red lillies, we first must establish the total amount Raymond can choose from as well as the amount of non-red lillies.

The total amount Raymond can choose from is the amount of bouqets. There are 8 red ones, 5 pink ones, and 7 violet ones. This means that there are 8+5+7=20 total bouquets.

The amount of non-red lillies is determined because we are asked to find the probability of selecting a non-red bouquet. We find the number of non-red bouquets by subtracting the total (20) by the number of red bouquets (8) to get 12.

Therefore, the total amount is 20 and the number of non-red bouquets is 12. Thus, if Raymond picks one bouquet, the probability of him selecting a non-red one is 12/20, or 3/5. The probability of him picking up a red bouquet, similarly, would be 8/20, as there are 8 options of red bouquets out of 20 total

Given:

The expression is:

[tex](6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)[/tex]

To find:

The resulting polynomial in standard form.

Solution:

We have,

[tex](6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)[/tex]

Write subtraction of a polynomial expression as addition of the additive inverse.

[tex](6m^5+3-m^3-4m)+(m^5-2m^3+4m-6)[/tex]

Rewrite terms that are subtracted as addition of the opposite.

[tex]6m^5+3+(-m^3)+(-4m)+m^5+(-2m^3)+4m+(-6)[/tex]

Group like terms.

[tex][6m^5+m^5]+[3+(-6)]+[(-m^3)+(-2m^3)]+[(-4m)+4m][/tex]

Combine like terms.

[tex]7m^5+(-3)+(-3m^3)+0[/tex]

On simplification, we get

[tex]7m^5-3-3m^3[/tex]

Write the polynomial in standard form.

[tex]7m^5-3m^3-3[/tex]

Therefore, the required polynomial in standard form is [tex]7m^5-3m^3-3[/tex].

Answer:

B.226

Step-by-step explanation:

I HOPE ITS HELP PO

Answer:

x = 20,

y = 15

m<1 = 75°

m<2 = 75°

m<3 = 75°

m<4 = 105°

Step-by-step explanation:

m<1 = 3x + 15

m<2 = 4x - 5

m<3 = 5y

✔️m<1 = m<2 (corresponding angles are congruent)

3x + 15 = 4x - 5 (substitution)

Collect like terms

3x - 4x = -15 - 5

-x = -20

Divide both sides by -1

x = 20

✔️m<3 = m<2 (corresponding angles are congruent)

5y = 4x - 5 (substitution)

Plug in the value of x and solve for y

5y = 4(20) - 5

5y = 80 - 5

5y = 75

5y/5 = 75/5

y = 15

✔️Find the measure of each labelled angle:

x = 20, y = 15

Thus:

m<1 = 3x + 15 = 3(20) + 15

m<1 = 75°

m<2 = 4x - 5 = 4(20) - 5

m<2 = 75°

m<3 = 5y = 5(15)

m<3 = 75°

m<4 + m<3 = 180° (same side interior angles are supplementary)

m<4 + 75° = 180° (substitution)

m<4 = 180° - 75° (subtraction property of equality)

m<4 = 105°

Answer:

31°,59°

Step-by-step explanation:

csc (2x+9)=sec(3x+26)

1/sin(2x+9)=1/cos (3x+26)

sin (2x+9)=cos(3x+26)

cos (90-2x-9)=cos(3x+26)

90=3x+26+2x+9

5x+35=90

5x=90-35=55

x=55/5=11

2x+9=2×11+9=31°

3x+26=3×11+26=59°

Answer:

5 units to the right

Step-by-step explanation:

(x-5) is considered as a horizontal shift and since it has got (-) you count to the right

Step-by-step explanation:

must be _1/27 in my opinion it's that

Answer:

768 m²

Step-by-step explanation:

8 x 400 = 3200 cm = 32 m

6 x 400 = 2400 cm = 24m

32 x 24 = 768 m²

Answer:

I think that a Cube Root Function

Step-by-step explanation:

Answer:

1 cup = 8 fl oz

Step-by-step explanation:

1 cup = 8 fl oz

Answer:

A: The bases of a triangular prism are equilateral triangles, since they have equal sides: 5, 5, and 5 yes, since if all lateral faces are rectangles, rectangles are formed from 4 perpendicular segments, thus, if all edges of the lateral faces are perpendicular, then they are rectangles

B:they have equal length sides and equal angles. For this to be true, the bases must be squares. Because it is a right prism, the lateral faces are rectangles.
C:If we have following equation right, then the angle between shorter sides is right angle:

13² = 12² + 5²

169 = 144 + 25

169 = 169

D:4*sqrt(2)

E: LSA of a cube = 100 in²

Step-by-step explanation:

Hope this helps

Answer:

[tex]{ \tt{from \: sine \: rule : }} \\ { \bf{ \frac{ \sin(A) }{A} = \frac{ \sin(B) }{B} }} \\ \\ { \bf{ \frac{ \sin(34 \degree) }{x} = \frac{ \sin(27 \degree) }{11} }} \\ \\ { \bf{x = \frac{11 \times \sin(34 \degree) }{ \sin(27 \degree) } }} \\ \\ { \tt{x = 13.5}}[/tex]

Answer:

7.50 + 14x < 60

x < 3.75

Step-by-step explanation:

Let

x = number of pizzas ordered

Delivery fee = $7.50

Cost per pizza = $14

Total cost should be less than $60

The inequality

7.50 + 14x < 60

14x < 60 - 7.50

14x < 52.5

x < 52.5/14

x < 3.75

Answer:

Part A

The volume of the triangular prism is 500 cm³

Part B

The total surface area of the prism is approximately 441.42 cm²

Step-by-step explanation:

The given details are;

The dimensions of the side length of the cube, s = 10 cm

The shape the cube was cut across to obtain = A prism

Part A

Whereby the prism obtained is a triangular prism, we have;

The cube can be cut in half to form a triangular prism

The volume of each triangular prism obtained = (1/2) × The volume of the cube

∴ The volume of the triangular prism = (1/2) × (10 cm)³ = 500 cm³

Part B

The height of the prism, h = 10 cm × sin(45°) = 5·√2 cm = (1/2) × The base width of the prism

The triangular cross sectional area of the prism, A₁ = 5·√2 × 5·√2 = 50

The square cross sectional area, A₂  = 10 × 10 = 100

The cross sectional area of the base, A₃ = 10·√2 × 10 = 100·√2

The total surface area of the prism, A = 2·A₁ + 2·A₂ + A₃

∴ A = 2×50 + 2×100 + 100·√2 = 300 + 100·√2 ≈ 441.42

The total surface area of the prism, A ≈ 441.42 cm²

Answer:

y=1x-4

Wait sorry I did it wrong the first time lol.

In standard Form, it should be 4x-4y=16

Step-by-step explanation:

yes yes hand me brain

Answer:

3/25 cup of butter

Step-by-step explanation:

You are baking a cake. The recipe asks for 3/5 cup of butter and you want to make 1/5 of the original recipe.

The calculation for the above question is given below:

1 recipe = 3/5 cup of butter

1/5 recipe = x

Cross Multiply

x × 1 recipe = 1/5 recipe × 3/5 cup of butter

x = 1/5 recipe × 3/5 cup of butter /1 recipe

x = 3/25 cup of butter

Therefore, you will need 3/25 cup of butter

Answer:

The second one from the top

Step-by-step explanation:

x^(5/3) y^1/3)

Answer:

you can rewrite expressions, for example

[tex] \sqrt[3]{x} = {x}^{ \frac{1}{3} } [/tex]

so yeah, option b is correct

Answer:

1) [tex]\frac{12.2}{sin(54)}[/tex] which rounds to 15.1

2) [tex]\frac{12.2}{cos(54)}[/tex] which rounds to 20.8

Step-by-step explanation:

1) We're going to have to use the trig ratios for this. We know that sin(x) = [tex]\frac{opposite}{hypotenuse}[/tex] (opposite side over the hypotenuse). In this case, we know that angle h = 54 and the side opposite to angle h = 12.2, and we're trying to find the hypotenuse. If we label the hypotenuse as x, then we can say that sin(H) = [tex]\frac{MI}{HI}[/tex]. We can plug in the values we know to get sin(54) = [tex]\frac{12.2}{x}[/tex]. From there, we multiply by x on both sides to get x out of the denominator, and then we divide by sin(54). So, we end up with x = [tex]\frac{12.2}{sin(54)}[/tex] which, if you put it in your calculator (and make sure the calculator is in degree mode) we get approximately 15.1 mi.

2) Follow the same steps that are described in 1), but instead of sin, we're using cos.

Hope this helps! Let me know if you have any further questions!

Step-by-step explanation:

15a)

[tex]x^2+4x=21[/tex]               Subtract both sides by 21

[tex]x^2+4x-21 =0[/tex]

15b)

7 and -3 multiply to -21 and add to 4

The factors are (x+7)(x-3)

15c)

x+7 =0

x=-7  

x-3=0

x=3              

Answer:

37.8 x 13.2 =4988.6

28,5 + 22.1 = 50.6

Answer:

30

Step-by-step explanation:

you need to multiply its length by its with

Answer:

56

Step-by-step explanation:

please I'm not sure about the answer above but I'll try to solve it and help you later

Answer:

12

Step-by-step explanation:

2+3=5+7=12

Given:

The expression is:

[tex]\sum\limits_{n=0}^{27}8n[/tex]

To find:

The expression that is equivalent to the given expression.

Solution:

According to the property of summation:

[tex]\sum\limits_{n=0}^{k}Cn=C\sum\limits_{n=0}^{k}n[/tex]

Where, C is a constant.

We have,

[tex]\sum\limits_{n=0}^{27}8n[/tex]

Using the above mentioned property of summation, we get

[tex]\sum\limits_{n=0}^{27}8n=8\sum\limits_{n=0}^{27}n[/tex]

The expression [tex]8\sum\limits_{n=0}^{27}n[/tex] is equivalent to the given expression.

Therefore, the correct option is C.

Answer:

(f + g) (x) = 14x-11

Step-by-step explanation:

From the question, what we have to do is to add the two given polynomials

We have this as;

(8x-7) + (6x-4) = 8x + 6x -7-4 = 14x -11

Answer:

B. f(x)= 2x-1

Step-by-step explanation:

The -1 is the y-intercept; 2x is the slope.

Answer:

The other sides equal 9cm also because a square has four equal sides.

L=9cm * W=9cm =A

A=81 cm

The probability of drawing two striped cubes in succession, without replacing the first cube drawn is

1/136​

Generally, The possibility of an occurrence may be quantified using the concept of probability. It is a number between 0 and 1, where 0 indicates that an event will never happen and 1 indicates that an event will definitely take place.

Probabilities may be represented as fractions, decimals, or percentages somewhere between 0 and 1, inclusive. In each given circumstance, the sum of the probabilities of all of the conceivable outcomes must equal 1.

The probability of drawing a striped cube on the first draw is 2/17 (there are 2 striped cubes out of a total of 17 cubes in the bag).  

The probability of drawing a second striped cube, given that the first one was not replaced, is 1/16 (there is now only 1 striped cube left in the bag out of a total of 16 remaining cubes).

The probability of both events happening is the product of the individual probabilities:

(2/17) * (1/16) =  1/136​

Read more about probability

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